Write a .Rmd Homework 7

Description

Write a .Rmd le to answer these questions, knitting it to .html along the way. Start by pasting this outline to help the grader nd your answers:

(Your Name Here)

• 1. Skin wounds

• 1a.

• 1b.

• 1c.

• 1d.

• 1e.

• 2. Test and power

• 2a.

• 2b.

• 2c.

• 1. Biologists studying the healing of skin wounds measured the rate at which new cells closed a cut made in the skin of an anesthetized newt. Here are data from a random sample of 18 newts, measured in micrometers (millionths of a meter) per hour:

29, 27, 34, 40, 22, 28, 14, 35, 26, 35, 12, 30, 23, 18, 11, 22, 23, 33

• 1. 1. Create a QQ plot of the data. Do you think it is reasonable to assume that the population distribution is normal? Explain your answer. (There isn’t a unique \right” answer.)

• 1. 2. Regardless of your answer to (a), assume the population distribution is normal and use that assumption to create a 90% CI for , the population mean rate.

• 1. 3. Consider a test of H₀ : = 25 vs. H_A : 6= 25 using signi cance level 0.10 (not the usual 0.05). Based on your 90% interval and no new calculations, say whether you would reject H₀.

• 1. 4. Test whether these data are strong evidence that the population mean rate is signi cantly greater than 25 at level = :05. (Note that you found a 90% con dence interval, not a 95% interval, and the interval was two-sided, but this test is one-sided, so the interval isn’t directly useful for deciding this test.) Use a p-value to decide the test.

• 1. 5. Suppose the problem statement included the addition, \Prior experience in the lab indicates that the population standard deviation is close to = 8 (micrometers per hour).” This would call for which changes to your con dence interval calculation? Write down the letters of all that are correct.

• 1. 1. 1. Replace x with _n^x .

        2. Replace t_17;:05 with z_:05 = 1:645.

p

iii. Replace n with n.

1. 1. • 4. Replace s (calculated from the data) with = 8.

1. 1. • 4. Replace s (calculated from the data) with ^p_n = ^p8₁₈ .

2. A random sample of size n = 10 is taken from a large population. Let be the unknown population mean. A test is planned of H₀ : = 12 vs. H_A : 6= 12 using = 0:1. A QQ plot indicates it it is reasonable to assume a normal population. From the sample, x = 14:2 and s = 4:88.

2. 1. Since the data leave it plausible that the population is normal, and the population standard deviation is unknown, a t-test is appropriate. Compute the p-value of the test. Do you reject or not reject H₀?

2. 2. Based on the test (and without calculating the interval), say whether you expect a 90% con dence interval to include 12.

2. 3. Using s = 4:88 as our best guess of (that is, pretending we know = 4:88), compute the power of a

future test of H₀ : = 12 vs. H_A : 6= 12 if the true population mean is _A = 15.

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